In an already known apparatus of this kind (DE-A 32 12 195), a transfer differential transmission situated on the transmission output and connected with both axles of the motor vehicle is locked by means of a multi-disc clutch in accordance with the parameters of the motor vehicle such as travel speed, steering angle, or engine torque. For said purpose, the multi-disc clutch is engaged by a hydraulic working pressure of a main control line against a disengaging spring, the working pressure in the main control line being adjusted as result of said parameters, by means of an electro-magnetically actuated pressure-control valve, and therewith the locking effect of the multi-disc clutch. A separate hydraulic system is provided for said actuation of the multi-disc clutch. Besides, upon actuation of the pressure-control valve in direction of the opening, vibrations can appear in the main control line pressure which lead to an indifferent control behavior of the whole pressure system.